While playing junior for the Selkirk Junior Fishermen in Winnipeg, Alex Shibicky was scouted by the New York Rangers who signed him in 1934. They promptly deposited him in the EHL with the Brooklyn Amateur Athletic Club. There he teamed up with his future NHL linemates, Mac and Neil Colville. The trio clicked with a promising show of offensive output.

After a short stint with the Rangers with 1935-36, Shibicky caught on for the long haul with the Blueshirts in 1936-37. In the company of the Colville brothers, the trio of youngsters absorbed every fine point of the game conveyed to them by the veteran Cook brothers. Soon the three sparkplugs were skating like bone fide NHLers.

As the decade advanced, the Rangers continued to add the pieces that would lead them down the Stanley Cup path. By 1939-40, the mix came together with an outstanding run, first past the Bruins and then the Leafs in the finals to claim the championship. While grappling against Toronto, Shibicky broke his ankle in three places, but kept the injury a secret. The team's doctor simply froze his leg up to the knee and sent him back onto the ice.

At the close of the 1941-42 campaign, Shibicky, like so many other NHLers, put his career aside to join the military for the duration of World War II. In 1945-46, he reclaimed his place on the Rangers' roster for 33 games and was then demoted to the Providence Reds of the AHL. The following year, he skated for the New Haven Ramblers of the same league and then hung his blades up for good at the end of the season.